Highest Common Factor of 669, 858, 625 using Euclid's algorithm

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

HCF Calculator using the Euclid Division Algorithm helps you to find the Highest common factor (HCF) easily for 669, 858, 625 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 669, 858, 625 is 1 the largest number which exactly divides all the numbers i.e. where the remainder is zero. Let us get into the working of this example.

Consider we have numbers 669, 858, 625 and we need to find the HCF of these numbers. To do so, we need to choose the largest integer first and then as per Euclid's Division Lemma a = bq + r where 0 ≤ r ≤ b

Highest common factor (HCF) of 669, 858, 625 is 1.

HCF(669, 858, 625) = 1

HCF of 669, 858, 625 using Euclid's algorithm

Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.

HCF of:

Highest common factor (HCF) of 669, 858, 625 is 1.

Highest Common Factor of 669,858,625 using Euclid's algorithm

Highest Common Factor of 669,858,625 is 1

Step 1: Since 858 > 669, we apply the division lemma to 858 and 669, to get

858 = 669 x 1 + 189

Step 2: Since the reminder 669 ≠ 0, we apply division lemma to 189 and 669, to get

669 = 189 x 3 + 102

Step 3: We consider the new divisor 189 and the new remainder 102, and apply the division lemma to get

189 = 102 x 1 + 87

We consider the new divisor 102 and the new remainder 87,and apply the division lemma to get

102 = 87 x 1 + 15

We consider the new divisor 87 and the new remainder 15,and apply the division lemma to get

87 = 15 x 5 + 12

We consider the new divisor 15 and the new remainder 12,and apply the division lemma to get

15 = 12 x 1 + 3

We consider the new divisor 12 and the new remainder 3,and apply the division lemma to get

12 = 3 x 4 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 669 and 858 is 3

Notice that 3 = HCF(12,3) = HCF(15,12) = HCF(87,15) = HCF(102,87) = HCF(189,102) = HCF(669,189) = HCF(858,669) .

We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma

Step 1: Since 625 > 3, we apply the division lemma to 625 and 3, to get

625 = 3 x 208 + 1

Step 2: Since the reminder 3 ≠ 0, we apply division lemma to 1 and 3, to get

3 = 1 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 3 and 625 is 1

Notice that 1 = HCF(3,1) = HCF(625,3) .

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Frequently Asked Questions on HCF of 669, 858, 625 using Euclid's Algorithm

1. What is the Euclid division algorithm?

Answer: Euclid's Division Algorithm is a technique to compute the Highest Common Factor (HCF) of given positive integers.

2. what is the HCF of 669, 858, 625?

Answer: HCF of 669, 858, 625 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 669, 858, 625 using Euclid's Algorithm?

Answer: For arbitrary numbers 669, 858, 625 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.